Quantum mechanics postulates that the hydrogen atom has a stable ground state from which it can be promoted to excited states by capture of electromagnetic radiation, with the energy of all possible states given by En = -13.598/n2 eV, in which n ≥ 1 is a positive integer. By contrast, it has been proposed that the n = 1 state is not the true ground state, and that so-called ‘hydrino’ states of lower energy can exist, which are characterized by fractional quantum numbers n = 1/p, in which 1 < p ≤ 137 is a limited integer1,2. Electron transition to a hydrino state, H(1/p) is non-radiative and requires a quantized amount of energy, 2mE1 (m is an integer), to be transferred to a catalyst3,4. Since its inception5 the hydrino hypothesis has remained highly controversial6-17 and laboratory verification studies by its proponents have been criticised18,19. Remarkably, no experimental testing by independent researchers has been described in the literature over the past 31 years. Here, we give an account of an independent electron paramagnetic resonance (EPR) study of molecular hydrino H2(1/4) that was produced by a plasma reaction of atomic hydrogen with non-hydrogen bonded water as the catalyst. A sharp, complex, multi-line EPR spectrum is found, whose detailed properties prove to be semi-quantitatively consistent with predictions20 from hydrino theory with an average error less than 0.09 G (0.2%) over a 39 G span of 37 lines. We have sought but failed to find reasonable alternative, ‘conventional’ interpretations for the detected paramagnetism. Fundamental relevance of the hydrino hypothesis lies in its challenging some of the foundations of the theory of quantum mechanics1. Very high net energy release during hydrino formation signifies technological relevance as a novel method of green energy production with recent validation at the 100 kW continuous power level by measurement of steam production20-27.